Question

A rums $1\frac{2}{3}$ times as fast as B.If A gives B a start of $80$ m, how must the winning post be so thats A and B might reach it at the same times?

• A. $200$ m
• B. $300$ m
• C. $270$ m
• D. $160$ m

Answer 1

The correct option is A $200$ m

$A$ runs $1\frac{2}{3}$ times as fast as $B$

Therefore ratio of the speeds of $A$ and $B=5:3$

Thus, in race of $5m$, $A$ gains $2m$ over $B$.

$2m$ is gained by $A$ in a race of $5m$.

$80m$ will be gained by $A$ in race of $\frac{5}{2}\times 80=200m$

$\Rightarrow$ Winning post is $200m$ away from the starting point.